|Sound pressure||p · SPL|
|Particle velocity||v · SVL|
|Sound intensity||I · SIL|
|Sound power level||SWL|
|Sound exposure level||SEL|
|Sound energy density||E|
|Sound energy flux||q|
|Speed of sound|
Particle displacement or displacement amplitude (represented in mathematics by the lower-case Greek letter ξ) is a measurement of distance of the movement of a particle from its equilibrium position in a medium as it transmits a wave. In most cases this is a longitudinal wave of pressure (such as sound), but it can also be a transverse wave, such as the vibration of a taut string. In the case of a sound wave travelling through air, the particle displacement is evident in the oscillations of air molecules with, and against, the direction in which the sound wave is travelling. A particle of the medium undergoes displacement according to the particle velocity of the wave traveling through the medium, while the sound wave itself moves at the speed of sound, equal to 343 m/s in air at 20 °C.
The instantaneous particle displacement ξ for a wave is:
If the wave is a standing wave or a traveling wave containing a single frequency, the particle displacement is:
This expression for undergoes simple harmonic oscillation, and as such is usually expressed as an RMS time average.
Particle displacement for a traveling wave containing a single frequency can be represented in terms of other measurements:
where in the above equation, the quantities may be taken throughout as rms time-averages (or all as maximum values). The single frequency traveling wave has acoustic impedance equal to the characteristic impedance, . Further representations for can be found from the above equations using the replacement .
|ξ||m, meters||Particle displacement|
|ω = 2πf||radians/s||angular frequency|
|p||Pa, pascals||sound pressure|
|Z0 = c · ρ||N·s/m3||characteristic impedance|
|Z = p / v||N·s/m3||acoustic impedance|
|c||m/s||Speed of sound|
|ρ||kg/m3||Density of air|
|E||W·s/m3||sound energy density|
|Pac||W, watts||sound power or acoustic power|
References and notes
- Julian W. Gardner, V. K. Varadan, Osama O. Awadelkarim (2001). Microsensors, MEMS, and Smart Devices. John Wiley and Sons. pp. 321–322. ISBN 978-0-471-86109-6.
- Arthur Schuster (1904). An Introduction to the Theory of Optics. London: Edward Arnold.
- John Eargle (January 2005). The Microphone Book: From mono to stereo to surround – a guide to microphone design and application. Burlington, Ma: Focal Press. p. 27. ISBN 978-0-240-51961-6.
- Wood, Robert Williams (1914). Physical optics. New York: The Macmillan Company.
- Strong, John Donovan; and Hayward, Roger (January 2004). Concepts of Classical Optics. Dover Publications. ISBN 978-0-486-43262-5.
- Barron, Randall F. (January 2003). Industrial noise control and acoustics. NYC, New York: CRC Press. pp. 79, 82, 83, 87. ISBN 978-0-8247-0701-9.